Abstract
We show that solutions to the periodic Cauchy problem for a family of non-linear evolution equations, which contains the Camassa-Holm equation, do not depend uniformly continuously on initial data in the Sobolev space $H^s(\mathbb{T})$, when $s=1$ or $s\geq 2$.
Citation
Erika A. Olson. "Non-uniform dependence on initial data for a family of non-linear evolution equations." Differential Integral Equations 19 (10) 1081 - 1102, 2006. https://doi.org/10.57262/die/1356050310
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